A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate

We report the observation of coherent circulation in a macroscopic Bose–Einstein condensate of polaritons in a ring geometry. Because they are spinor condensates, half-quanta are allowed in where there is a phase rotation of π in connection with a polarization vector rotation of π around a closed path. This half-quantum behavior is clearly seen in the experimental observations of the polarization rotation around the ring. In our ring geometry, the half-quantum state that we see is one in which the handedness of the spin flips from one side of the ring to the other side in addition to the rotation of the linear polarization component; such a state is allowed in a ring geometry but will not occur in a simply connected geometry. This state is lower in energy than a half-quantum state with no change of the spin direction and corresponds to a superposition of two different elementary half-quantum states. The direction of circulation of the flow around the ring fluctuates randomly between clockwise and counterclockwise from one shot to the next; this fluctuation corresponds to spontaneous breaking of time-reversal symmetry in the system. This type of macroscopic polariton ring condensate allows for the possibility of direct control of the circulation to excite higher quantized states and the creation of Josephson junction tunneling barriers.Ring condensates, analogous to superconducting rings, have received much attention lately (1–9); among other predictions, a ring condensate allows the possibility of macroscopic superposition of states with different circulation. A ring condensate is topologically distinct from a condensate in a simply connected region.With the advance of the field of polariton condensates in the past few years, it is a natural step to create a condensate ring in a microcavity polariton system. The polariton system allows direct, nondestructive observation of the momentum distribution, energy distribution, and spatial distribution of the particles as well as direct measurement of the coherence properties through interferometry. To make a macroscopic ring requires macroscopic transport distances as well as macroscopic coherence length. Macroscopic coherence has been achieved with polaritons with coherent motion over tens of micrometers with lifetimes of 10–20 ps (10, 11) and coherent motion over hundreds of micrometers with lifetimes of 150–200 ps (12–14). One advantage of the long-lifetime polariton systems is that the polaritons can move well away from the laser spot where they are generated, so that the laser can be viewed as a simple source term and does not interact with the condensate. General reviews of previous polariton work with shorter transport distances are in refs. 15–19.The polaritons can be viewed as photons that have been given a small effective mass of the order of 10^?4 times the mass of a vacuum electron and repulsive interactions, which are about 10⁴ times stronger than the typical χ⁽³⁾ nonlinearities of photons in solids. The effective mass comes from the dispersion of the photons in a planar cavity, ℏω=ℏc(k∥2+k⊥)1/2, where k_⊥ is fixed by the width of the cavity, which implies that ℏω≃E0+ℏ2k∥2/2meff with m_eff = ?k_⊥/c for low k_∥. There are two circular polarization modes of the cavity photons corresponding to m = ±1 for the projection of the angular momentum on the z axis perpendicular to the plane. The strong interactions between photons are generated by mixing the photon states with a sharp excitonic resonance in a semiconductor inside the cavity, so that the photons pick up a fraction of the exciton–exciton interaction. Although their interactions are much stronger than the interactions of typical photons in a solid medium, the polaritons are still in the weakly interacting Bose gas regime.The structure for these experiments is a planar cavity, in which the mirrors are distributed Bragg reflectors of AlAs/AlGaAs and the exciton medium consists of GaAs/AlGaAs quantum wells embedded in this cavity. This structure has the same design as that used in previous experiments, which allows coherent transport of polaritons over hundreds of micrometers in the 2D plane of the cavity (12–14). Recent measurements (14) give the cavity lifetime as 135 ps, which corresponds to a polariton lifetime of 200 ps or more. Although this lifetime may seem to be short compared with atoms evaporating from an optical trap on timescales of seconds, the polariton lifetime is sufficient for them to interact many times with each other. In these long-lifetime polariton systems, the ratio of lifetime in the trap to the particle–particle collision time can be of the order of 500:1, comparable with the ratio for cold atom condensates.The lifetime of the polaritons and the strength of the interaction between the polaritons can be tuned by varying the energy difference between the photon states and the exciton states (known as the “detuning”), which leads to a varying degree of mixing of the photons and excitons. Because the planar cavity has a wedge that gives a gradient of cavity width, we can tune the strength of the polariton–polariton interactions simply by choosing different locations on the sample with different cavity width. There is a tradeoff in how much excitonic interaction character to give to the polaritons. Fewer interactions (more photon-like) allow long transport length, whereas more interactions allow better thermalization of the polariton gas through collisions and longer population lifetime.